2 Answers
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It is common for real royal houses and other nobility to have a motto, which is usually displayed on their coat of arms. For instance "Je Maintiendrai", "I will maintain", for the House of Orange, the Dutch royal house.

It's a tradition in the U.S. as well - each state has an official state motto - "Manly deeds, womanly words", "Let the welfare of the people be the supreme law", "To be, rather than to seem", etc.
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Joe L.Jun 25 '14 at 20:23

mot·to [mot-oh]noun, plural mot·toes, mot·tos.
1. a maxim adopted as an expression of the guiding principle of a person, organization, city, etc.
2. a sentence, phrase, or word expressing the spirit or purpose of a person, organization, city, etc., and often inscribed on a badge, banner, etc.

[emphasis added is mine]

This has a two-fold meaning and purpose.

Guiding Principle
These mottoes are used as a means of conveying at the most basic level to their fellows that "this is how we live" or "this is how you should model your life".

In other words, it is engraved into the minds and mentalities of children right from an early age, it helps to shape and define them - labels affect who we are1, 2, 3.

So a child who grows up in an environment where they are constantly being told that they should not "plant seeds" but merely "reap the rewards" which others have wrought, then that child is undoubtedly going to turn into a Reaver - "We Do Not Sow".

Spirit or Purpose
In their purest forms, mottoes stand to tell those around them what they are about and in many cases serve as a warning ("watch out; I don't work for my goods, I kill for them").

A Stark will tell you that "Winter is Coming"4 (and also that winter is pretty much always coming); which serves as a dire warning to those surrounding them and is a grim reminder that life in the North is difficult, especially in the winter.

A Lannister will tell you that they pay all of their debts (unofficial motto); this means that they pay all debts whether good or bad! As demonstrated multiple times by multiple Lannisters. "Hear me Roar" I believe is a tribute of their cunning and ambitiousness.

A Bolton will tell you "Our Blades Are Sharp" which is a fair warning "we flay our enemies, and Our Blades are Sharp, so don't mess around"!

I do believe that GRRM did intend for his mottoes to have a similar effect and meaning.

Ned frowned. “He must learn to face his fears. He will not be three forever. And winter is coming.”“Yes,” Catelyn agreed. The words gave her a chill, as they always did. The Stark words. Every noble house had its words. Family mottoes, touchstones, prayers of sorts, they boasted of honor and glory, promised loyalty and truth, swore faith and courage. All but the Starks. Winter is coming, said the Stark words. Not for the first time, she reflected on what a strange people these northerners were.-A Song of Ice and Fire: A Game of Thrones, Chapter Two (Catelyn).

Nice answer, but do you really need to use a spoiler tag on a one sentence conversation from the 2nd chapter of the 1st book? Your description reveals more about the Stark words than the quote itself.
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DacioJun 26 '14 at 15:08

Good answer, I almost feel it was too detailed though - surely the quote from GoT (Catelyn's POV) alone would have served as a good in-universe answer for why the House words exist?
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The Giant of LannisterJun 26 '14 at 19:22

@TheGiantofLannister Yes for In-Universe, but I wanted to focus more on the Out-of-Universe
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MoozJun 26 '14 at 21:50